Probability
Probability
nta_abhyas_2025
Grade 12
Question:
The probability distribution of a random variable $X$ is given as
| $X$ | $-5$ | $-4$ | $-3$ | $-2$ | $-1$ | $0$ | $1$ | $2$ | $3$ | $4$ | $5$ |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| $P(X)$ | $p$ | $2p$ | $3p$ | $4p$ | $5p$ | $7p$ | $9p$ | $10p$ | $11p$ | $12p$ |
Then, the value of $p$ is
\frac{32}{35}
\frac{1}{32}
\frac{35}{32}
\frac{32}{35}
Step-by-Step Solution
Key Concept: The sum of all probabilities in a probability distribution must equal 1.
Sum of Probabilities = 1, so $p + 2p + 3p + 4p + 5p + 7p + 8p + 9p + 10p + 11p + 12p = 1$. This gives $72p = 1 = p = \frac{1}{72}$.
Correct Answer: 1